Comparative Statics Analysis

1. Comparative Statics Analysis • This chapter studies how people change their choices when conditions such as income or changes in the prices of goods change.

2. Demand Function • The elements that determine the quantity demanded are the prices of X and Y, the person’s income (I), and the person’s preferences for X and Y. • Assume preferences do not change during the analysis.

3. Homogeneous Demand Function • Individual demand functions are homogeneous since quantity demanded does not change when prices and income increase in the same proportion. • The budget constraint PXX + PYY = I is identical to the budget constraint 2PXX + 2PYY = 2I. • Graphically the lines are the same.

4. Changes in Income • When a person’s income increase the budget line shifts out from I1 to I2 to I3. • The slope of the budget lines are the same since the prices have not changed .

5. FIGURE 3.1: Effect of Increasing Income on Quantities of X and Y Chosen Quantity of Y per week Y3 Y2 U3 U2 Y1 U1 I1 I2 I3 Quantity of X per week 0 X1 X2 X3

6. Normal Goods • A normal good is one that is bought in greater quantities as income increases. • If the quantity increases more rapidly than income the good is called a luxury good as with good Y in Figure 3.1. • If the quantity increases less rapidly than income the good is called a necessity good as with good X in Figure 3.1.

7. APPLICATION 3.1: Engel’s Law • In general, the fraction of income spent on food declines as income increases. • This finding was discovered by Prussian economists Ernst Engel (1821-1896).

8. TABLE 1: Percentage of Total Expenditures of Various Items in Belgian Families in 1853

9. TABLE 2: Percentage of Total Expenditures by U.S. Consumers on Various Items, 1997

10. Inferior Goods • An inferior good is one that is bought in smaller quantities as income increases.

11. FIGURE 3.2: Indifference Curve Map Showing Inferiority Quantity of Y per week Y3 U3 Y2 U2 Y1 U1 I1 I2 I3 Z2 Z1 0 Z3 Quantity of Z per week

12. Changes in a Good’s Price • A change in a good’s price alters both the slope and intercept of the budget line. • A change in quantity demanded that is caused by substitution of one good for another is called the substitution effect. • A change in quantity demanded caused by a change in real income is the income effect.

13. FIGURE 3.3: Income and Substitution Effects of a Fall in Price Quantity of Y per week Old budget constraint Y* B New budget constraint U1 0 X* XB Quantity of X per week Substitution effect

14. FIGURE 3.3: Income and Substitution Effects of a Fall in Price Quantity of Y per week Old budget constraint Y** Y* U2 B New budget constraint U1 0 X* XB X** Quantity of X per week Substitution effect Income effect Total increase in X

15. The Effects Combined • Using the hamburger-soft drink example from Chapter 2, suppose the price of soft drinks falls from $.50 to $.25. • Previously the consumer could purchase up to 20 soft drinks, but now he or she can purchase up to 40. • This price decrease shifts the budget line outward and increases utility.

16. The Effects Combined • If the consumer bought his or her previous choice it would now cost $7.50 so that $2.50 would be unspent. • If the individual stayed on the old indifference curve he or she would equate MRS to the new price ratio (consuming 1 hamburger and 4 soft drinks). • This move is the substitution effect.

17. Substitution and Income Effects from an Increase in Price • An increase in PX will shift the budget line in as shown in Figure 3.4. • The substitution effect, holding “real” income constant, is the move on U2 from X*, Y* to point B. • Because the higher price causes purchasing power to decrease, the movement from B to X**, Y** is the income effect.

18. FIGURE 3.4: Income and Substitution Effects of an Increase in Price Quantity of Y per week U2 New budget constraint Y* Old budget constraint 0 X* Quantity of X per week

19. FIGURE 3.4: Income and Substitution Effects of an Increase in Price Quantity of Y per week U2 U1 B New budget constraint Y* Old budget constraint 0 XB X* Quantity of X per week Substitution effect

20. FIGURE 3.4: Income and Substitution Effects of an Increase in Price Quantity of Y per week U2 U1 B Y** New budget constraint Y* Old budget constraint 0 X** XB X* Quantity of X per week Income effect Substitution effect Total reduction in X

21. Substitution and Income Effects from an Increase in Price • In Figure 3.4, both the substitution and income effects cause the individual to purchase less soft drinks do to the higher price of soft drinks.

22. Substitution and Income Effects for a Normal Good: Summary • As shown in Figures 3.3 and 3.4, the substitution and income effects work in the same direction with a normal good. • When the price falls, both the substitution and income effects result in more purchased. • When the price increases, both the substitution and income effects result in less purchased.

23. Substitution and Income Effects for a Normal Good: Summary • This provides the rational for drawing downward sloping demand curves. • This also helps to determine the steepness of the demand curve. • If either the substitution or income effects are large, the change in quantity demanded will be large with a given price change.

24. Substitution and Income Effects for a Normal Good: Summary • If the substitution and income effects are small, the effect of a given price change in the quantity demanded will also be small. • This kind of analysis also offers a number of insights about some commonly used economic statistics.

25. APPLICATION 3.2: The Consumer Price Index and Its Biases • The Bureau of Labor Statistics calculates the (CPI) as a principal measure of inflation. • To construct the CPI, a typical basket of goods purchased by consumers in the base year (currently 1982) is calculated. The ratio of the current cost of the basket to the 1982 price is the value of the CPI. • The rate of change in the CPI between two periods is the reported rate of inflation

26. An Algebraic Example • The CPI is defined as the ratio of the costs of these two market baskets • If the basket cost $100 in 1982 prices and $175 in 2002, the value of the CPI would be 1.75 and with a measured 75 percent increase in prices over the 20 year period.

27. Substitution Bias in the CPI • The CPI does not take into account the real possibility that consumers would substitute among commodities because of changes in relative prices. • In Figure 1, the typical individual is initially consuming X82, Y82 maximizing utility on U1 with 1982 constraint I.

28. FIGURE 1: Substitution Bias of the Consumer Price Index Quantity of Y per year Y82 U1 I’ I I” 0 X82 Quantity of X per year

29. New Product Bias in the CPI • New products typically experience sharp declines in prices and rapidly grow in rates of acceptance. • If the CPI does not include these new products, this source of welfare increase is omitted. • The CPI basket is revised but not rapidly enough to eliminate this bias.

30. Outlet Bias in the CPI • The typical basket is bought at the same retail outlets every month. • This method can omit the benefits of sales or other bargains. • The CPI does not currently take such price-reducing strategies and thus tends to overstate inflation.

31. Consequences of the CPI Biases • There is a general agreement that the CPI overstates inflation by as much as 0.75 to 1.0 percent per year. • Politicians have proposed caps on government Cost of Living Adjustments (COLAs) tied to the CPI but none have been enacted. However, in the private sector few COLAs provide full offsets to inflation measured by the CPI.

32. Substitution and Income Effects for Inferior Goods • With an inferior good, the substitution effect and the income effects work in opposite directions. • The substitution effect results in decreased consumption for a price increase and increased consumption for a price decrease.

33. FIGURE 3.5: Income and Substitution Effects for an Inferior Good Quantity of Y per week B New budget constraint Y* U2 Y** Old budget constraint U1 0 Quantity of X per week X** X*

34. Giffen’s Paradox • If the income effect of a price change is strong enough with an inferior good, it is possible for the quantity demanded to change in the same direction as the price change. • Legend has it that this phenomenon was observed by English economist Robert Giffen.

35. The Lump Sum Principle • The intuitive explanation of the lump-sum principle is that a single-commodity tax affects people in two ways: • it reduces their purchasing power, • it directs consumption away from the good being taxed. • The lump-sum tax only has the first of these two effects.

36. Generalizations of the Lump-Sum Principle • The utility loss associated with taxing will be minimized by taxing goods for which the substitution effect is small. • Even though the tax will reduce purchasing power, it will minimize the impact of directing consumption away from the good being taxed.

37. FIGURE 3.7: Effect on the Demand for Y from a Decrease in the Price of X: Substitutes Quantity of Y per week Old budget constraint Y* Y** B New budget constraint U2 U1 0 Quantity of X per week X* X**

38. Complements • Two goods are complements if an increase in the price of one causes a decrease in the demanded of the other or vice versa.

39. Substitutes • Two goods such that if the price of one increases, the demand for the other rises are substitutes.

40. FIGURE 3.8: Construction of an Individual’s Demand Curve Quantity of Y per week Budget constraint for P 9 X U 1 0 X’ Quantity of X per week (a) Individual ’ s indifference curve map Price P 9 X 0 X’ Quantity of X per week (b) Demand curve

41. FIGURE 3.8: Construction of an Individual’s Demand Curve Quantity of Y per week Budget constraint for P 9 X Budget constraint for P 0 X - X U 2 U 1 0 X’ X” X’” Quantity of X per week (a) Individual ’ s indifference curve map Price P 9 X P 0 X 0 X’ X” Quantity of X per week (b) Demand curve

42. FIGURE 3.8: Construction of an Individual’s Demand Curve Quantity of Y per week Budget constraint for P 9 X Budget constraint for P 0 X Budget constraint for P - X U 3 U 2 U 1 0 X’ X” X’” Quantity of X per week (a) Individual ’ s indifference curve map Price P 9 X P 0 X P - X 0 X’ X” X’” Quantity of X per week (b) Demand curve

43. FIGURE 3.8: Construction of an Individual’s Demand Curve Quantity of Y per week Budget constraint for P 9 X Budget constraint for P 0 X Budget constraint for P - X U 3 U 2 U 1 0 X’ X” X’” Quantity of X per week (a) Individual ’ s indifference curve map Price P 9 X P 0 X P - X d X 0 X’ X” X’” Quantity of X per week (b) Demand curve

44. Consumer Surplus • The extra value individuals receive from consuming a good over what they pay for it is called consumer surplus.

45. APPLICATION 3.6: Valuing Clean Air • By looking at the ceteris paribus relationship between air pollution levels in various locations and the prices of houses in these locations, it is possible to infer the amount that people will pay to avoid dirty air. • This information allows the computation of a compensated demand curve for clean air.

46. APPLICATION 3.6: Valuing Clean Air • In Figure 1, the vertical axis shows the price home buyers are willing to pay to avoid air pollution and the horizontal axis shows the quantity of clean air purchased. • The national average is reflected at point E as home buyers pay $50 and consume an average of 55 micrograms of suspended particulates per cubic meter.

47. FIGURE 1: Compensated Demand Curve for Clean Air Price ($) 85 80 60 E 50 40 20 D Air quality (mg/m3) 100 75 50 25 0 55

48. APPLICATION 3.6: Valuing Clean Air • Consumers are paying $2,250 ($50 times 45 micrograms) extra to avoid dirty air. • At E0 consumers also receive a consumer surplus equal to the shaded area in Figure 1. • This consumer surplus of 788 per household can be multiplied by the total number of households to estimate total consumer surplus from clean air.